Question

6.It is being given that the points A(1, 2), B(0,0) and C(a, b) are collinear.Which of the following relations between a and b is true?
(A) a = 2b
(B) 2a = b
(C) a+b=0
(D) a-b=0
7.The value of theta for which sin (44° +theta) = cos 30°, is
(A) 46°
(B) 60°
(C) 16°
(D) 90°
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Answer 1

Answer:

7. Answer is C & 6. Answer isA

Answer 2

6. The following relations between a and b is true?

(B) 2a = b

7.The value of theta for which sin (44° +theta) = cos 30°, is

(C) 16°

6)

A (1,2) , B (0,0) , C (a,b)

If the three points are colliear, then the triangle formed using the points would have zero area.

So,

Area = (1/2) [x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)]

where,

x₁ = 1

x₂ = 0

x₃ = a

y₁ = 2

y₂ = 0

y₃ = b

Replacing the values, we get

Area = (1/2) [1(0-b) + 0(b-2) + a(2-0)]

⇒ (1/2) [-b + 0 + 2a] = 0

⇒ 2a - b = 0

⇒ 2a = b

So, option (B) is correct.

7)

sin (44° + θ°) = cos 30°

We know, cos θ = sin (90-θ)°

⇒ sin (44° + θ°) = sin (60°)

Thus,

44° + θ° = 60°

⇒ θ° = 60° - 44° = 16°

So, option (C) is correct.